This application relates to gaming machines and, in particular, to video gaming machines of the type which simulate real physical games. The application relates in particular to techniques for operating such video gaming machines and for developing pay tables therefor.
A number of physical games involve the movement of one or more objects on a play field. Such games may include pinball, pachinko, roulette, craps and the like. Each of these games is initiated by placing an object in motion in accordance with a set of initial conditions and proceeding to one of a plurality of outcomes corresponding, respectively, to final resting conditions of the object or objects.
In pachinko and pinball, the object is a ball which is launched onto a play field with a particular velocity in a particular direction and, perhaps, with a particular spin. These initial conditions determine the initial trajectory of the ball. The trajectory and velocity of the ball are changed en route by obstacles in the play field, such as pins or pegs or flippers or the like. Plural balls may simultaneously be traveling along the play field, particularly in pachinko. The fundamental difference between pachinko and pinball is that, in pachinko, the trajectory-changing obstacles in the play field are fixed and passive, whereas in pinball they may be movable and active and, indeed, may be player-controllable. In a game such as roulette, which is played with a single ball, the play field itself, which includes a rotatable roulette wheel, is movable relative to a fixed reference, in addition to the ball being movable relative to the play field, both the ball and the wheel being placed into motion by a croupier. In craps, the object is a cubical die with numbered faces, the game being initiated by a player manually casting a pair of dice onto the play field. In games such as pachinko and craps, wherein plural objects simultaneously occupy the play field, the routes of the objects are complicated by the fact that they can collide with each other. The details of play of these games will be well understood by those of ordinary skill in the gaming arts. In such real physical games, there is no need for a pay table to determine the outcome or the win amount. Rather, they rely on actual physical resting conditions of the objects. However, in an electronic version of such games on a video platform, a method of producing and reliably evaluating a pay table is required.
Prior video gaming machines which simulate such real physical games as those described above have provided a storage medium which stores a plurality of xe2x80x9cplaysxe2x80x9d of the game, such as a plurality of different object routes from a starting condition to a final outcome. Win amounts are assigned to each of these stored xe2x80x9cplaysxe2x80x9d. A play is initiated by a player xe2x80x9cdepositingxe2x80x9d a wager amount and activating the machine, which then randomly selects one of the stored object routes and displays it on a video display and then awards the player the corresponding win amount. The display may include a background display of the play field, as well as a superimposed display of the randomly selected object route. The object routes could be stored, for example, by videotaping actual plays of physical games and storing them in analog or digital form. A drawback of this approach is that the number of object routes which can be stored is rather limited. Thus, during an extended player session at the machine, a particular route, and therefore, outcome, may occur more than once, seriously detracting from the randomness and, therefore, the realism of the game.
This application relates to video gaming machines and methods of operating such machines which avoid the disadvantages of prior video gaming techniques while affording additional structural and operating advantages.
An important aspect is the provision of a video gaming machine of the type which simulates a real physical game, and which more realistically simulates the randomness of the real physical game.
Another aspect is the provision of a video gaming machine which is based on a mathematical model of a real physical game.
Another aspect is the provision of a method for accurately developing a pay table for a modeled game on a video gaming platform.
Certain ones of these and other aspects may be obtained by providing a method of operating a video gaming machine which simulates a real physical game initiated by placing an object in motion in accordance with a set of initial conditions and proceeding to one of a plurality of outcomes corresponding respectively to final resting conditions of the object, the method comprising: establishing in software a mathematical model of the game including a plurality of rules governing movement of the object once it is placed in motion, establishing a range of possible values for each of a plurality of parameters, randomly selecting for each parameter a value from its associated range of values to establish the set of initial conditions, running the set of initial conditions through the model for simulating movement of the object to a final resting condition to determine the outcome, and displaying the simulated movement of the object.
Further aspects may be attained by providing a method of operating a video gaming machine which simulates a real physical game initiated by placing an object in motion in accordance with a set of initial conditions and proceeding along a route to one of a plurality of outcomes corresponding respectively to final resting conditions of the object, the method comprising: determining a finite collection of points on a play field including a route starting point and at least one route end point corresponding to a final resting condition and a finite collection of possible paths of the object from one point to another such that each point except route end points may have one or more paths leading away from it, assigning a probability of occurrence to each path and to each point, randomly selecting a path from among the paths leading away from the route starting point in accordance with their probabilities of occurrence, causing the object to traverse the selected path to the point it leads to, then randomly selecting a path from among the paths starting at the point at which the object is currently located in accordance with their probabilities of occurrence, then repeating the preceding two steps until a route end point is reached, and displaying the simulated movement of the object from route staring point to the route end point.
Still other aspects may be attained by providing a video gaming machine which simulates a real physical game initiated by placing an object in motion in accordance with a set of initial conditions and proceeding to one of a plurality of outcomes corresponding respectively to final resting conditions of the object, the gaming machine comprising: a player input device for activating the game, a display device, a processor operating under control of a stored program and responsive to the input device for controlling the display device, a memory device coupled to the processor and storing a mathematical model of the game including a plurality of rules governing movement of the object once it is placed in motion, and a pay table of win amounts respectively corresponding to different outcomes, and a payout mechanism, the processor program including a first routine responsive to a player input for randomly determining an origin state and running it through the model for simulating movement of the object to a final resting condition to determine an outcome and controlling the display device to display the simulated movement of the object, and a second routine for determining from the pay table a win amount corresponding to the outcome and actuating the payout mechanism to award that amount to the player.
Still other aspects may be attained by providing a method of developing a pay table for a video gaming machine which simulates a real physical game initiated by placing an object in motion in accordance with a set of initial conditions and proceeding to one of a plurality of outcomes corresponding respectively to final resting conditions of the object, the method comprising: establishing in software a mathematical model of the game including a plurality of rules governing movement of the object once it is placed in motion, creating a list of outcomes, assigning a probability of occurrence to each outcome, assigning a win amount to each outcome, and determining a pay table percentage by multiplying each outcome""s probability of occurrence by its win amount and summing the products for all of the outcomes in the list.